Imprint of the black hole singularity on thermal two-point functions

TL;DR

This paper investigates how black hole singularities influence thermal two-point functions in holographic theories, revealing exponentially small nonperturbative effects linked to null geodesics bouncing off the singularity.

Contribution

It introduces a bulk WKB approach to compute reflection coefficients at the black hole singularity and connects these to corrections in high-frequency expansions of two-point functions.

Findings

Nonperturbative corrections are exponentially suppressed in high-frequency expansions.

Null geodesics bouncing off the singularity control these nonperturbative effects.

A bulk WKB method is developed to calculate reflection coefficients at the singularity.

Abstract

We consider two-point functions of light fields at finite temperature and large real frequencies in holographic theories. The thermal system is dual to a single-sided AdS black hole. We show that the high-frequency expansion obtained from the Operator Product Expansion receives exponentially small nonperturbative corrections, which are controlled by null geodesics bouncing off the black hole singularity in the two-sided eternal black hole geometry. We develop a bulk WKB description of these bouncing geodesics and explain how to calculate reflection coefficients at the singularity.